Turn off all air conditioning / heating units.
Unplug any appliances that make noise (refrigerators, fans, etc).
If you are in a highly reverberant space, make sure you close mic your actors. Remember, reverb can always be added in post, but it cannot be subtracted!
For example, as I type this I am sitting in my kitchen and am acutely aware of the sound of the refrigerator - a sound that most people would be totally unconscious of. I was once shooting a scene at a local video store and had made sure that the air conditioning was turned off before calling action. However, halfway into the night one of the actors turned the a/c back on without telling me. I was so caught up in directing the actors I did not even notice until I had shot a good additional hour worth of takes. I mention this just to point out that certain sounds kind of "fade into the background" when we are shooting to the point we don't even notice them. However, when we load up the footage back in the edit suite, what was once "in the background" is now "front and center."
It is amazing how much better digital noise reduction technology has gotten over the last few years. However, sounds that change over time (such as a plane flying overhead or different cars driving by) are difficult to remove without causing obvious artifacts in the processed audio. This usually manifests itself as a "hollow" or "tinny" character to the processed dialogue. Right now I am working on the sound design for a film that is set in an underwater research station. Unfortunately, the set was located close to a local airport. Several sound takes have the sound of airplanes or local traffic intruding on the track. Obviously, it would not do to hear a plane flying overhead when you are supposed to be in an undersea research vessel! In most cases I am able to remove this type of noise, however, it does add more time and expense to the post-production process.
The reverb issue is very real, too, as many low-budget filmmakers end up using the camera mic to capture their audio. This can be acceptable in a small space that is fairly dead acoustically. But using the camera mic in a large reverberant space such as a warehouse guarantees that the resulting dialogue recording will be almost completely unintelligible (this is true even if you have a great quality standalone mic that is too far from the actors). This means you will need to pay for an ADR session during post, or that the low budget origins of your sound will be immediately evident to anyone watching your screener. And nothing pulls a viewer out of the film experience more quickly than bad quality sound - especially when your audience is straining to understand the dialogue!
Another issue for post sound editors is overlapping dialogue. While overlapping dialogue can be a great stylistic choice, it can be an unsolvable problem in post if the director / editor wants to make any changes to the original flow of the scene, or wants to use Take 12 of character A and combine it with Take 5 of character B. Complicating this even further is that many directors who like the authenticity of overlapping dialogue also like the spontaneity of allowing their actors to ad lib some of their lines. While I personally think this style helps enhance a film when the director is going for a documentary-type feel, it can be a real problem trying to get all of the sound takes to match. A partial solution is to body mic your actors so that the individual actors dialogue is available as a separate track with little bleed from the other actors. The other solution is to record separate takes of each actor without the dialogue actually overlapping in the same environment. That way it is sometimes possible to extract a word here or there from the separate takes to clean up an improperly overlapping cut.
Hope all of this helps!